Calculus of Variations and Geometric Measure Theory

M. Santilli

When all parallel sets of a $ C^1 $-hypersurface are nowhere $ C^1 $-regular

created by santilli on 03 May 2026

[BibTeX]

Submitted Paper

Inserted: 3 may 2026

Year: 2026

ArXiv: 2604.26764 PDF
Links: arxiv link

Abstract:

We prove a necessary and sufficient condition for a $ C^1 $-hypersurface to have all parallel sets nowhere $ C^1 $-regular. As a corollary, we deduce that for a generic $ C^1 $-regular convex body all interior parallel bodies have nowhere $ C^1 $-regular boundaries.